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The[ClickHereforSampleQuestions]Theweightedmeanformulabelowcanbeusedtocalculatetheweightedmeanforanon-negativesetofdatawithnonnegativeweightsSolution:Herethex-valuesarethepriceofthegivenfoodstuffandtheweightsassociatedarethequantities(inKg)Then,theWeightedarithmetic meanSixnumbersWecouldthinkthateachofthosenumbershasa"weight"of¼(becausetherearenumbers):Mean=¼×+¼×+¼×+¼×4StepTogetthe sumofweightedterms,multiplyeachaveragebythenumberofstudentsthathadthataverageandthensumthemup×+×=+=StepTotalnumberofterms=Total numberofstudents=StepUsingtheformula,Answer:TheaveragescoreofthewholeclassisBecareful!Thescoresareweightedasfollows:QuizHWExam1 Exam2Final%%%%%Supposeyouraveragesareasfollows:QuizHWExam1Exam2Final%%%%%MeanHereisthemeanof1,2,andAddupthenumbers, dividebyhowmanynumbers:Mean=+++==WeightsDemonstratethefinancialefficiencyofhigh-rankingofficialsNow,Answer:Theimportanceofthecostof capitalisasfollows:Evaluationofinvestmentproject.a){9,3,,5,2/5,3}c){math,english,science,math,history,math,english}IV.MiscellaneousGivean exampleofasetwherethemodeislessthanthemean.SupposeTofindtheweightedaverage(orweightedmean)ofadataset,multiplyeachvaluebyitsweight andaddtheproductstogether,thendividebythesumoftheweightsDeterminethebestcapitalstructureWeoftendothisincomputingcoursegrades–eg, weightingthefinalexamtwiceasmuchasamidtermexamWEIGHTEDAVERAGEAveragingitemswithdifferentweightsExample:CalculatinggradesSuppose aclasshasquizzes,homeworkandthreeexamsa){3,,9,,}c){1,5,,,}Illthemode(s)ineachsetWhenwedoasimplemean(oraverage),wegiveequal weighttoeachnumberThemostcommonexampleofaweightedaverageisaschoolgradeWhatisthemeanofthesevennumberstogether?IlFindthemedian ofeachsetChoosingasourceoffundingSolution:Asweknow,thefirstprimenumbersare2,3,5,7,,,,,,andHere,ThesumofobservationsFindthegeometric meanof2,6,9,5,Solution:Givendatavalues,6,9,5,andWeknowthattheformulatofindthegeometricmeanis(a₁×a₂××aₙ)1/n.Theaverageofnumbersis theaverageoftwoofthemis,whiletheaverageoftheothertwoisFindthearithmeticmeanofthefirstprimenumbersn,withnonnegativeweightsw,w,,w4, WEIGHTEDAVERAGEAveragingitemswithdifferentweightsExample:CalculatinggradesSupposeaclasshasquizzes,homeworkandthreeexams=(wx+A weightedaverageisameancomposedofsmallermeansthatdonotevenlycontributetothewholeWeightedaveragesSupposetheweightofthemid-term examinationis,theweightsofeachoffourprojectsis,andtheweightofthefinalexaminationisSupposeyourmid-termgradeis,yourgradesinyourfourprojects are,,andWeightedAveragesWorksheet]Consideracoursewherequizzesare%ofthegrade,examis%,examis%,homeworkis%,andthefinalis%Forasetof datax,x,,xn,theweightedaverageis xwGiveanexampleofasetwhereToformaweightedmeanofnumbers,wefirstmultiplyeachnumberbyanumber (“weight”)forthatnumber,thenaddupalltheweightednumbers,thendividebythesumoftheweights.EstablishadebtpolicyWhatisherfinal"weighted average"?Establishadividendpolicy